12

How Air Velocity AffectsThe Thermal Performance of Heat Sinks: A Comparison of Straight Fin, Pin Fin and maxiFLOWTM Architectures

Introduction

A device’s temperature affects its op-erational performance and lifetime. To achieve a desired device temperature, the heat dissipated by the device must be transferred along some path to the environment [1]. The most common method for transferring this heat is by finned metal devices, otherwise known as heat sinks.

Resistance to heat transfer is called thermal resistance. The thermal resis-tance of a heat sink decreases with more heat transfer area. However, be-cause device and equipment sizes are decreasing, heat sink sizes are also growing smaller. On the other hand, device heat dissipation is increasing. Therefore, designing a heat transfer path in a limited space that minimizes thermal resistance is critical to the ef-fective design of electronic equipment.

This article discusses the effects of air flow velocity on the experimentally de-termined thermal resistance of different heat sink designs. To be able to com-pare these designs, we need to first review basic heat transfer theory as applied to heat sinks. Previously pub-lished work is discussed, along with

heat sink selection criteria.The heat transfer rate of a heat sink, , depends on the difference between the component case temperature, Tc, and the air temperature, Ta, along with the total thermal resistance, Rt. This rela-tionship is shown in Equation 1. For a basic heat sink design, as shown in Figure 1, the total thermal resistance depends on the sum of the heat sink resistance, Rhs, the spreading resis-tance in the heat sink base, Rsp, and the thermal interface resistance from the component to the heat sink base,

RTIM, as shown in Equation 2.

(1)

where

(2)

Therefore, to compare different heat sink designs, the thermal interface re-sistance, RTIM, and the spreading resis-tance, Rsp, was similar among the heat sinks tested.

Heat sink

Component case, Tc

Base

Air, Ta

TIM

Component Q

Rhs

Rsp

RTIM .

Figure 1. Exploded View of a Straight Fin Heat Sink with Corresponding Thermal Resis-tance Diagram.

Q = (Thot - Tcold)/Rt = (Tc - Ta)/Rt

.

Rt = RTIM + Rsp + Rhs

Q.

13October 2008 |Qpedia

For this study, the same thermal in-terface material (TIM) was used with all heat sinks. This minimized the dif-ference in the thermal interface resis-tance, RTIM, between heat sink tests. As is normal, the spreading resistance of a heat sink’s base, Rsp, increased with de-creasing base thickness and conductiv-ity. It also increased with an increasing difference in the heat sink base area and the heat dissipation area [2].

Lasance and Eggink have provided a method to rank a heat sink for certain applications [3]. This measurement is based on extracting the average heat transfer coefficients from time-depen-dant temperature curves as a function of velocity and bypass. The measured effective heat transfer coefficient is then scaled by mass, volume, weight or height. This provides several per-formance metrics to give designers a novel way to rank heat sinks in con-ditions that resemble an application. Heat sinks with heights between 5 and 20 mm were tested [3]. In addition to varying heights, the heat sink base thickness varied from 1.2 to 3 mm. The base width and length varied from 42.2 to 49.8 mm. The ratio between the width and length of the heat sink also varied, i.e. both square and rectangular base shapes were used. ATS maxiFLOWTM and pin fin heat sinks were tested, with the maxiFLOWTM series showing the lowest thermal resistance [3].

Forghan, et.al. also discuss the thermal resistance of various heat sink designs [4]. They conducted their tests based

on the steady state temperature of the heat sinks, unlike Lasance and Egg-ink, whose test are based on transient data. The maxiFLOWTM heat sinks were found to have the lowest thermal resistance, especially for air flow veloc-ity below 2 m/s [4].

The heat sinks tests in this article were conducted in a wind tunnel and the data points were taken at steady state values. The heat sinks were selected based on the following heat sink selec-tion criteria:

The same thermal interface mate-rial was used for all the heat sink

1.

tests.The base thickness, width, and length were the same for all the heat sinks tested. The same size heat source area was used for the different heat sink tests.The heat sinks had the same fin height.

About the Heat Sinks Tested Heat sinks with 42 x 42 mm and with 27 x 27 mm base nominal dimensions were selected, as they are common sizes used in electronics cooling. Fin types included straight fin, pin fin, elliptical fin and ATS’ maxiFLOW, as

2.

3.

4.

Table 1. Types of Heat Sinks Tested, With Their Dimensions and Mass.

# Heat Sink Type L [mm]

w [mm]

H [mm] Part No. Mass,

m (g)

1 Cylindrical Pin Fin (CPF) 42 42 24 CPF4224 32

2 Elliptical Pin Fin (EPF) 42.5 42.5 33 EPF4233 36

3 Cylindrical Pin Fin (CPF) 25 25 25 CPF2525 12

4 maxiFLOWTM 42.5 42.5 17.5 MF4217 28

5 maxiFLOWTM 25 25 17.5 MF2517 12

6 Elliptical Pin Fin (EPF) 25 25 33 EPF2533 12

7 Straight Fin (SF) 42.5 42.5 17.5 SF4217 18

8 Straight Fin (SF) 27 27 17.5 SF2517 10

9 Elliptical Pin Fin (EPF) 42 42 17 EPF4217 24

10 Elliptical Pin Fin (EPF) 25 25 17 EPF2517 18

THerMAL AnALySiS

(a) (c) (d) (b)

shown in Table 1 along with dimensions, part numbers and mass. Figure 2 shows some of the selected heat sinks.

For testing purposes, a thermocouple hole was drilled into the center of the base of each heat sink, on the side per-pendicular to the air flow direction in which each was tested. The position of a thermocouple hole can be seen in Figure 3.

Wind tunnel test section(CWT-106)

Wind tunnel fans

Inlet

Power supplies

WTC-100Wind Tunnel Controlller

PC

Data logger

L

H w

Thermocouple hole

Air flow direction

Figure 3. Illustration of a Straight Fin Heat Sink.

Figure 2. Various Heat Sinks Types Tested: Straight Fin (a), Elliptical Pin Fin (b), Cylindrical Pin Fin (c), and ATS’ maxiFLOW™ (d).

Figure 4. The ATS CWT-106 Open Loop Wind Tunnel and WTC-100 Wind Tunnel Controller.

Experimental Set-Up of the Heat Sinks in a Wind TunnelThe natural and forced convection thermal resistances of each heat sink were determined in an ATS CWT-106™ open loop wind tunnel managed by a WTC-100 wind tunnel con-troller (Figures 4, 5, 6). Heater pads of 25 x 25 mm were placed in the center of the heat sinks to provide the heat sources. The heat sinks were mounted in the wind tunnel test section. Air flow and temperature were measured 15 cm

upstream of the heat sink. Thermal paste was applied before the thermocouple was inserted into the hole.

15October 2008 |Qpedia

Test ProcedureAfter being set-up for testing as de-scribed in Section 2, heat dissipated by the heater pad was transferred to the air by natural convection. The heat sink base temperature and inlet air temper-ature were monitored until steady tem-perature state occurred. At this time, the heat sink base and inlet air temper-atures were recorded, along with the voltage supplied to each heater pad.

For forced convection, steady state val-ues were recorded at a range of air flow velocities. Power input for the 42 mm heat sinks was 12 W, while for the 27 mm heat sinks the power ranged from 6 to 9 W.

Processed ResultsThe heat sinks were compared based on their thermal resistances. The heat transfer rate from heat sink base to air is given by Equation 3 (below). From here, the heat sink’s thermal resistance is calculated using Equation 4. This as-sumes that the heat transferred by the sink to the air is equal to the power in-put to the heat source. After applying Equation 4 to the experimental data, the results are plotted in Figures 7 and 8.

(3)

(4)

Figure 7 shows that heat sink thermal resistance decreases for natural con-vection. The maxiFLOWTM heat sinks had the lowest thermal resistance for natural convection of the sinks tested. The 33 mm elliptical pin fin heat sinks

Air flow velocity direction

Wind tunnel test section lid

Heat sink

Wind tunnel test section back wall

Thermocouple wires

Selotape

Chomerics T405

Heater pad

152 52

Gravity

PCB test piece Heater pad wires

Insulating board

Figure 5. Illustration of the Experiment Set-up Inside the Wind Tunnel Test Section.

Figure 6. The Wind Tunnel Test Section. Heat Sinks EPF4233 and CPF4225 are Mounted Side by Side.

had a higher thermal resistance than the maxiFLOW heat sink, and the 17 mm elliptical pin fins had the highest thermal resistance. The 25 mm cylin-

drical pin fin heat sinks had about the same thermal resistance as the straight fin heat sinks. If it had been possible to cut the cylindrical pin fin heat sinks to

Q = (Tb - Ta)/R.

R = (Tb - Ta)/P

THerMAL AnALySiS

16

a height of 17 mm, they would have had a higher thermal resistance than the straight fin heat sinks.

For forced convection, Figure 8 shows that the thermal resis-tance of all the heat sinks tested decreased with increased air flow rate. A 33 mm tall EPF had the lowest thermal resis-

(a)(a) (b)(b)Advanced Thermal Solutions, Inc. 89-27 Access Road | Norwood, MA | USAT: 781.769.2800 | F: 769.769.9979 |www.qats.com

Boards running hot?LeT The expeRTS AT ATS Show yoU how To eNSURe pRodUcT ReLIABILITy, Speed TIMe-To-MARkeT ANd RedUce coSTS wITh expeRT TheRMAL MANAgeMeNT ANALySIS ANd deSIgN SeRvIceS.

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7 8 9

Input power, P [W]

Hea

t sin

k th

erm

al re

sist

ance

, R [K

/W]

CPF4224EPF4233MF4217SF4217EPF4217

0

5

10

15

20

25

30

0 0.5 1 1.5 2 2.5 3 3.5

Input power, P [W]

Hea

t sin

k th

erm

al re

sist

ance

, R

[K/W

]

CPF2525EPF2533MF2517SF2517EPF2517

tance. However, once they were cut to a height of 17 mm, they had the highest thermal resistance. This was similar to the natural convection tests. After the 33 mm EPF, the maxi-FLOW heat sinks had the best thermal resistance. The 42 mm straight fin and cylindrical pin fin heat sinks had similar thermal resistances.

Figure 7. Thermal Resistance of 27 mm (a) and 42 mm (b) Heat Sinks for Natural Convection, Plotted Against Input Power.

1717October 2008 |Qpedia

Advanced Thermal Solutions, Inc. 89-27 Access Road | Norwood, MA | USAT: 781.769.2800 | F: 769.769.9979 |www.qats.com

Boards running hot?LeT The expeRTS AT ATS Show yoU how To eNSURe pRodUcT ReLIABILITy, Speed TIMe-To-MARkeT ANd RedUce coSTS wITh expeRT TheRMAL MANAgeMeNT ANALySIS ANd deSIgN SeRvIceS.

0

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5 3 3.5

Air velocity, V [m/s]

Hea

t sin

k th

erm

al re

sist

ance

, R [K

/W]

CPF2525EPF2533MF2517SF2517EPF2517

0

1

2

3

4

5

6

7

0 0.5 1 1.5 2 2.5 3 3.5

Air velocity, V [m/s]

Hea

t sin

k th

erm

al re

sist

ance

, R [K

/W]

CPF4224EPF4233MF4217SF4217EPF4217

A criterion for the heat sink selection was that the sinks be the same height. However, the cylindrical pin fin heat sinks were 25 mm high. A possible scaling method is to calculate the heat transfer coefficient, h, for a heat sink. The heat transfer coefficient was then used to calculate the new thermal re-sistance of a shorter heat sink of the same type. To calculate the heat trans-fer coefficient, it was assumed that the heat sink base temperature measured was the fin base temperature and that the fin had a thermal efficiency of 100%, i.e. the fin tip had the same tem-

Figure 8. Thermal Resistance of 27 mm (a) and 42 mm (b) Heat Sinks for Forced Convection, Plotted Against Air Flow Velocity.

perature as the fin base. For the heat sinks tested, the thermal efficiency was in the order of 98%. Therefore, it was valid to assume that the thermal effi-ciency of the fin was 100%. Modifying Equation 3 resulted in Equation 7. The heat transfer coefficient was then cal-culated using Equation 8.

(7)

(8)

Each heat sink was first measured and the heat transfer area, AHT, was cal-

culated. This area was then used in Equation 8. Because elliptical pin fins were tested at two heights, their results were used to verify that the method used to scale the heat sinks was valid. The results for the natural convection tests appear in Figure 9. They show that there was not a good relationship between the heat sinks of the same base dimensions. For a specific heat sink base size, the heat transfer coef-ficient for the elliptical pin fin heat sinks differed by 25%. This is shown in Fig-ure 9 (b).

0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5 6 7 8 9

Input power, P [W]

Hea

t sin

k he

at tr

ansf

er c

oeffi

cien

t, h

[W/m

²·K]

CPF2525CPF4224EPF2533EPF4233MF2517MF4217SF2517SF4217EPF2517EPF4217

0

1

2

3

4

5

6

7

8

9

0 1 2 3 4 5 6

Input power, P [W]

Hea

t sin

k he

at tr

ansf

er c

oeffi

cien

t, h

[W/m

²·K] EPF2533

EPF4233EPF2517EPF4217

Figure 9. Heat Transfer Coefficients for Natural convection.

Q = (Tb - Ti)/R = hAHT (Tb-Ti).

HT

1h RA=

THerMAL AnALySiS

18

Figure 10 shows the heat transfer co-efficient data for the forced convection tests. Figure 10 (b) shows that the heat transfer coefficient for elliptical pin fin heat sinks with 42 mm base dimen-sions differed by an average of 1.6%. For a 25 mm base, the difference was on average 13.7%. This indicates that the heat transfer coefficient can be used to scale a heat sink. However, this may only be used for heat sinks of the same type and heat sink base area.Using the heat transfer coefficient cal-culated for the cylindrical pin fin heat

0

10

20

30

40

50

60

70

80

0 0.5 1 1.5 2 2.5 3 3.5

Air velocity, V [m/s]

Hea

t sin

k he

at tr

ansf

er c

oeffi

cien

t, h

[W/m

²·K]

CPF2525CPF4224EPF2533EPF4233MF2517MF4217SF2517SF4217EPF2517EPF4217

0

10

20

30

40

50

60

70

0 0.5 1 1.5 2 2.5 3 3.5

Air velocity, V [m/s]

Hea

t sin

k he

at tr

ansf

er c

oeffi

cien

t, h

[W/m

²·K] EPF2533

EPF4233EPF2517EPF4217

Figure 10. Overall Heat Transfer Coefficients for Forced Convection.

sink, the thermal resistance of a 17 mm high heat sink was estimated. These values are plotted in Figure 11 with the thermal resistance values of the other 17 mm high heat sinks. Figure 11 shows that the maxiFLOW heat sinks had the best thermal resistance for 17 mm high heat sinks, followed by the straight fin sinks. The elliptical and cylindrical pin fin heat sinks had the highest thermal resistance of the sinks tested. Figure 11 also shows that the maxiFLOW heat sink were especially effective at air flow velocities below 1.5 to 2 m/s.

Having shown that it was not possible to scale the heat sinks for natural con-vection, Figure 12 shows the thermal resistance of the 17 mm high heat sink for natural convection.

SummaryBy documenting the experimental performance of various types of heat sinks, it was found that for the same base dimensions and fin height, maxi-FLOW heat sinks had the lowest ther-mal resistance. Straight fin heat sinks had a higher thermal resistance than

0

2

4

6

8

10

12

0 0.5 1 1.5 2 2.5 3 3.5

Air velocity, V [m/s]

Hea

t sin

k th

erm

al re

sist

ance

, R [K

/W]

MF2517SF2517EPF2517CPF2517

0

1

2

3

4

5

6

7

8

0 0.5 1 1.5 2 2.5 3 3.5

Air velocity, V [m/s]

Hea

t sin

k th

erm

al re

sist

ance

, R [K

/W]

MF4217SF4217EPF4217CPF4217

Figure 11. Heat Sink Thermal Resistance for 17 mm High Heat Sinks for Forced Convection. The Values of the Cylindrical Pin Fin Heat Sinks Are Based on the Overall Heat Transfer Coefficient Values of the Taller Heat Sink.

May 2008 |Qpedia 1919

the maxiFLOWTM heat sinks. Cylindrical and elliptical pin fin heat sinks had the worst thermal resistance of the heat sinks tested.

References:

Sergent, J. and Krum, A., Thermal Management Hand-book for Electronic Assemblies, First Edition, McGraw-Hill, 1998.Qpedia Thermal eMagazine, Spreading Thermal Resis-tance; Its Definition and Control, Vol. 1, Issue 7, 2007.Lasance, C., and Eggink, H., A Method to Rank Heat Sinks in Practice: The Heat Sink Performance Tester, Semiconductor Thermal Measurement and Manage-ment Symposium, IEEE, 2005.

1.

2.

3.

0

2

4

6

8

10

12

14

16

0 1 2 3 4 5 6 7 8 9

Input power, P [W]

Hea

t sin

k th

erm

al re

sist

ance

, R [K

/W]

MF4217SF4217EPF4217

0

5

10

15

20

25

30

0 0.5 1 1.5 2 2.5 3 3.5

Input power, P [W]

Hea

t sin

k th

erm

al re

sist

ance

, R [K

/W]

MF2517SF2517EPF2517

Figure 12. Thermal Resistance of 17 mm High Heat Sink, For the 27 mm (a) and 42 mm (b) Heat Sinks For Natural Convection, Plotted Against Input Power.

Is it hot in there?Advanced Thermal Solutions, Inc. 89-27 Access Road | Norwood, MA | 02062 | USAT: 781.769.2800 | F: 769.769.9979 |www.qats.com

Learn more about ats’ thermaL Design anD testing services by visiting www.qats.com or caLL 781.769.2800.

Forghan, F., Goldthwaite, D., Ulinski, M., and Metghal-chi, H., Experimental and Theoretical Investigation of Thermal Performance of Heat Sinks, ISME, 2001

4.